tetration exp(z)-1+k

[tommy1729]

The tangent superfunction provides an excellent piecemeal definition of tetration, and when it replaces the linear approximation, the resulting sexp(z) approximation has a continuous first and second derivative. This works for all tetration bases.

There are many nonlinear approximations that give a continuous first and second derivative.
Why is this preferred ? Is there a uniqueness condition ?

What is the advantage of this over just fitting the derivatives at the connection points ? ( Like A Robbins rediscovered )

regards

tommy1729